Reading Assignments -
Math 104 - Calculus II
March 1998
I'll use Maple syntax for mathematical notation on this page.
Be sure to check back often, because the assignments may change.
For March 2
Section 8.3 Arclength
- To read: All
- Be sure to understand:
The statement of the Fact at the bottom of page 468, and Example 2.
We'll talk about the section How Long is Cn? in class.
Email Subject Line: Math 104 3/2 Your Name
Reading Question:
Use the Fact on page 468 to set up the integral that gives the length of the
curve y=x3 from x=1 to x=3.
For March 4
Section 10.1 When Is an Integral Improper?
- To read: All
- Be sure to understand:
Examples 1, 2, and 4. The formal definitions of convergence and divergence
on pages 523 and 524.
Email Subject Line: Math 104 3/4 Your Name
Reading Questions:
- What are the two ways in which an integral may be improper?
- Explain why int( 1/x2, x=1..infty) is improper. Does the integral converge or diverge?
- Explain why int( 1/x2, x=0..1) is improper. Does the integral converge or diverge?
For March 6
Work on Project 2 today. No Reading Assignment.
For March 9
Section 10.2 Detecting Convergence, Estimating Limits
- To read: Through Example 5
- Be sure to understand:
Example 2 and the statement of Theorem 1
Email Subject Line: Math 104 3/9 Your Name
Reading Questions:
- If 0 < f(x) < g(x) and int( g(x), x=1. . infty) converges, will int(f(x), x=1. .infty)
converge or diverge? Why?
- There are two types of errors that arise in Example 2 for approximating
int( 1/(x5 +1), x=1..infty). What are the two types?
For March 11
Section 10.2 Detecting Convergence, Estimating Limits (continued)
- To read: The remainder of the section.
- Be sure to understand:
The statement of Theorem 2
Email Subject Line: Math 104 3/11 Your Name
Reading Questions:
Suppose that 0 < f(x) < g(x).
- If int(f(x), x=1. .infty) diverges, what can you conclude about int( g(x), x=1. . infty)?
- If int(g(x), x=1. .infty) diverges, what can you conclude about int( f(x), x=1. . infty)?
For March 13
Section 10.4 l'Hopital's Rule: Comparing Rates
- To read: All, but you may skip the
section on Fine Print: Pointers Toward a Proof. We'll talk about a
different justification during class.
- Be sure to understand:
The statement of Theorem 3, l'Hopital's Rule.
Email Subject Line: Math 104 3/13 Your Name
Reading Questions:
- Does l'Hopital's Rule apply to lim(x -> infty) x2 / ex ?
Why or why not?
- Does l'Hopital's Rule apply to lim(x -> infty) x2 / sin(x) ?
Why or why not?
March 16 - 20
Spring Break
For March 23
First day after Spring Break, so No Reading Assignment.
For March 25
Section 11.1 Sequences and Their Limits
- To read: Through page 557 and the statements of Theorem 2 and Theorem 3.
- Be sure to understand:
The section of Fine Points on page 553, the statements of Theorems 2 and 3.
Email Subject Line: Math 104 3/25 Your Name
Reading Questions:
- Does the following sequence converge or diverge? Be sure to explain your answer.
1, 3, 5, 7, 9, 11, 13, . . .
- Find a symbolic expression for the general term ak of the sequence
1, -2, 4, -8, 16, -32, . . .
For March 27
Exam 2 today. No Reading Assignment.
For March 30
Section 11.2 Infinite Series, Convergence, and Divergence
- To read: Through Example 4. This can be tough going.
- Be sure to understand:
The section Series Language: Terms, Partial Sums, Tails, Convergence, Limit on page 563
Email Subject Line: Math 104 3/30 Your Name
Reading Questions:
- There are two sequences associated with every series. What are they?
- Does the geometric series (1/2)k converge or diverge?
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